Answer:
The cost is a fixed $2, plus $3.25 for any additional hour.
Then if you rent it for x hours, the cost is:
c(x) = $2 + $3.25*x
Is this situation continuous or discrete?
Yes, it is discrete, because x is "the number of hours"
so if you rent it for 1.30 hours, they will say "ok, this is equivalent to two hours".
This means that while the values of x are continuous, the possible costs are:
{$2, $2 + $3.25, $2 + 2*$3.25, ....}
Which is a discrete set.
Then the sign for 1 to 5 hours will be:
1 hour ---------- $2 + $3.25 = $5.25
2 hours -------- $2 + 2*$3.25 = $8.50
3 hours--------- $2 + 3*$3.25 = $11.75
4 hours--------- $2 + 4*$3.25 = $15
5 hours -------- $2 + 5*$3.25 = $18.25
In the other park the cost is only $4 for each hour (no fixed cost) then the total cost for x hours is:
c(x) = $4*x
Now, which option is better?
If we look at the costs for different numbers of hours for this other equation, we have:
1 hour ----- $4
2 hours ---- 2*$4 = $8
3 hours ----- 3*$4 = $12
4 hours ------ 4*$4 = $16
Then: if you want to skate 2 hours or less, Skate City is cheaper, if you want to skate more than that, kate Days is cheaper.
This happens because the first one has a smaller slope, meaning that is larger at first, but as x grows the price does not grow as much as in Skate City
